In some states, Mr. Trump has surprised establishment-aligned Republicans with his breadth of support beyond the less-educated men who form his base. Even so, his support in the nominating process, in which some 30 million people may ultimately vote, would be swamped in a general election, when turnout is likely to be four times that.

“We’re talking about somebody who has the passionate devotion of a minority and alternately scares, appalls, angers — or all of the above — a majority of the country,”said Henry Olsen, a conservative analyst. “This isn’t anything but a historic election defeat just waiting to happen.”

What could ensure a humiliating loss for Mr. Trump in November are his troubles with constituencies that have favored Republicans in recent elections. Among independents, a group that Mitt Romney carried even as he lost to President Obama in 2012, Mr. Trump would begin the fall campaign at a considerable disadvantage: 19 percent have a favorable opinion of him, but 57 percent view him unfavorably, the Times/CBS survey found. Given his loathed standing among Democrats and the possibility that many in his own party would spurn him, Mr. Trump would need to invert his numbers among independents to even be competitive in November.

With white women, a bloc Mr. Romney easily won even in defeat, Mr. Trump is nearly as unpopular: 23 percent view him favorably, while 54 percent have an unfavorable opinion of him. And that was before Mr. Trump attacked Senator Ted Cruz’s wife, ridiculed a female reporter against whom Mr. Trump’s campaign manager was charged with committing battery, and suggested that women who have abortions should face criminal punishment before reversing himself.

Mr. Trump’s penchant to offend and his household-name celebrity are a potentially lethal combination, as most voters have both firm and deeply negative opinions of him. His incendiary comments about minorities and the disabled, and proposals to bar Muslims from entering the United States or to force Mexico to pay for a wall on the southern border, have resounded so widely that half of all voters said they would be scared if he were elected president, according to the Times/CBS poll.

“There is no precedent for this,” said Neil Newhouse, a veteran Republican pollster. “In the modern polling era, since around World War II, there hasn’t been a more unpopular potential presidential nominee than Donald Trump.”

Stan Greenberg, the longtime Democratic pollster, released a survey Friday summing up Mr. Trump’s vulnerabilities under the headline, “Earthquake?” Mr. Trump trails Mrs. Clinton by 23 points among women in Mr. Greenberg’s poll, suggesting the possibility of a gender gap of historic proportions. (The Times survey last month had Mrs. Clinton leading by 20 points among women.) The largest gender gap in the last 36 years was Bob Dole’s 11-point loss among women against Bill Clinton in 1996.

“His gains with men have been neutralized with women,” Mr. Greenberg said of Mr. Trump. “There’s no play here. The math just doesn’t work.”

Nationally, Mrs. Clinton leads Mr. Trump by about 10 percentage points in most head-to-head polls — the widest margin at this point in a presidential campaign in 16 years.

If Mrs. Clinton somehow loses the Democratic race — unlikely given her delegate advantage — Mr. Trump could fare even worse in a general election against Senator Bernie Sanders of Vermont, who has higher margins than Mrs. Clinton in head-to-head polling against Mr. Trump in most swing states.

Even among the working-class whites, who have been the foundation of his success in the Republican primaries, Mr. Trump would enter the general election with substantial difficulties. He is viewed unfavorably by a majority of whites without college degrees, according to an ABC News/Washington Post poll early last month.

It is possible that Mr. Trump could improve his standing with blue-collar voters who are crucial in Rust Belt states like Pennsylvania and Wisconsin, where polls now show him faring worse than Mr. Romney did in 2012. But doing so would not be cost-free.

“By leaning into white grievance politics, you give back whatever gains you made as you move up the economic scale,” said Liam Donovan, a Republican strategist who has written extensively on Mr. Trump’s vulnerabilities.

“There just aren’t enough votes left in the places where Trump could be strong, like rural areas, to offset the vote-rich places where Trump repels.”

Or, as Mr. Olsen put it, referring to Michigan:

“If you bring in 30,000 blue-collar voters from Flint, but you lose 50,000 from suburban Detroit, you’ve not helped yourself very much.”

This losing trade-off has been largely overlooked because of Mr. Trump’s success so far and the failure of more affluent Republican primary voters to unite behind any of his rivals.

But the general-election universe is vastly larger and more diverse than the Republican primary electorate. There are likely to be around 30 million votes in this year’s Republican primary once all 56 states and territories finish voting in June. In the 2012 contest between Mr. Obama and Mr. Romney, about 129 million voters cast ballots.

“You’re talking about a significantly more conservative, partisan, older and whiter group of voters than the general electorate,” Mr. Newhouse said. “It’s like night and day.”

Mr. Trump’s hopes rest largely on his energizing a coalition of the disaffected: millions of people who have not voted in recent elections but who have found in Mr. Trump someone giving voice to their anger. High primary turnouts have fed speculation that Mr. Trump could lure back the so-called missing white voters — populist-minded Americans thought to have skipped the 2012 presidential election, and who, depending on their numbers, offer a glimmer of hope for many conservatives in an era of unfavorable demographic shifts.

But Mr. Trump cannot count on such a surge. The actual number of missing white voters is quite low in the closely contested states, where turnout remained high or even rose in 2012.

Moreover, there is scant evidence that white voters who did stay home would be inclined to support Mr. Trump. In fact, they were far younger and much more likely to be registered Democrats than the white voters who did turn out, according to the census and data from L2, a nonpartisan voter file vendor.